FULL ASYMPTOTIC EXPANSIONS FOR THIN ELASTIC FREE PLATES

The case of a linearly elastic plate with free boundary conditions on the lateral side is investigated as the half-thickness epsilon tends t o zero. As in hard clamped plates, the generic leading term of the asy mptotic expansion of the scaled displacement is a Kirchhoff-Love field with in-plane generating functions satisfying classical bending and m embrane problems of Neumann type (compare with [1]). The first boundar y layer profile is of bending type, so that in the case of a membrane load the convergence of the three-dimensional solution to the two-dime nsional limit one is of improved accuracy. Conditions under which the asymptotic expansion 'starts later' are given and the structure of the first non-vanishing term is studied. (C) Academie des Sciences/Elsevi er, Paris.